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Investment Securities (Tables) | 9 Months Ended
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Sep. 30, 2018
Investments, Debt and Equity Securities [Abstract] |
Pre-tax net investment income | The following table presents pre-tax net investment income for the three and nine months ended September 30, 2018 and 2017.
|  | Three Months Ended |  | Nine Months Ended
|  | September 30, |  | September 30,
Millions |  | 2018 |  | 2017 |  | 2018 |  | 2017
Investment income: |  |  |  |  |  |  |  |
Fixed maturity investments |  | $ | 7.5 |  |  | $ | 9.8 |  |  | $ | 27.3 |  |  | $ | 32.9 |
Short-term investments |  | 1.8 |  |  | .3 |  |  | 6.5 |  |  | .6 |
Common equity securities |  | 3.4 |  |  | 2.7 |  |  | 11.2 |  |  | 7.7 |
Other long-term investments |  | 1.2 |  |  | .1 |  |  | 1.7 |  |  | .5 |
Total investment income |  | 13.9 |  |  | 12.9 |  |  | 46.7 |  |  | 41.7 |
Third-party investment expenses |  | (.5 | ) |  | (.7 | ) |  | (1.8 | ) |  | (2.0 | )
Net investment income, pre-tax |  | $ | 13.4 |  |  | $ | 12.2 |  |  | $ | 44.9 |  |  | $ | 39.7 |
Schedule of Realized and Unrealized Gain (Loss) on Investments | The following table presents net realized and unrealized investment gains (losses) for the three and nine months ended September 30, 2018 and 2017:
|  | Three Months Ended | Nine Months Ended
|  | September 30, | September 30,
Millions |  | 2018 |  | 2017 | 2018 |  | 2017
Net realized investment (losses) gains, pre-tax |  | $ | (10.2 | ) |  | $ | 6.8 |  | $ | (13.9 | ) |  | $ | 20.8 |
Net unrealized investment gains, pre-tax |  | 76.3 |  |  | 25.7 |  | 36.8 |  |  | 81.7 |
Net realized and unrealized investment gains, pre-tax |  | 66.1 |  |  | 32.5 |  | 22.9 |  |  | 102.5 |
Income tax expense attributable to net realized and unrealized investment gains |  | (9.7 | ) |  | (3.9 | ) | (5.9 | ) |  | (9.5 | )
Net realized and unrealized investment gains, after-tax |  | $ | 56.4 |  |  | $ | 28.6 |  | $ | 17.0 |  |  | $ | 93.0 |
Schedule of realized gain (loss) on investments | The following tables present net realized investment gains (losses) for the three and nine months ended September 30, 2018 and 2017
|  | Three Months Ended |  | Three Months Ended
|  | September 30, 2018 |  | September 30, 2017
Millions |  | Net realized losses |  | Net foreign exchange gains (losses) |  | Total net realized losses reflected in earnings |  | Net realized gains (losses) |  | Net foreign exchange gains (losses) |  | Total net realized gains (losses) reflected in earnings
Fixed maturity investments |  | $ | (5.1 | ) |  | $ | — |  |  | $ | (5.1 | ) |  | $ | .6 |  |  | $ | 1.2 |  |  | $ | 1.8 |
Short-term investments |  | — |  |  | — |  |  | — |  |  | (.1 | ) |  | — |  |  | (.1 | )
Common equity securities |  | (1.5 | ) |  | — |  |  | (1.5 | ) |  | 4.9 |  |  | 5.4 |  |  | 10.3 |
Other long-term investments |  | (3.6 | ) |  | — |  |  | (3.6 | ) |  | 2.0 |  |  | (7.2 | ) |  | (5.2 | )
Net realized investment (losses) gains, pre-tax |  | (10.2 | ) |  | — |  |  | (10.2 | ) |  | 7.4 |  |  | (.6 | ) |  | 6.8 |
Income tax benefit (expense) attributable to net realized investment (losses) gains |  | 2.3 |  |  | — |  |  | 2.3 |  |  | (.6 | ) |  | — |  |  | (.6 | )
Net realized investment (losses) gains, after-tax |  | $ | (7.9 | ) |  | $ | — |  |  | $ | (7.9 | ) |  | $ | 6.8 |  |  | $ | (.6 | ) |  | $ | 6.2 |
|  | Nine Months Ended |  | Nine Months Ended
|  | September 30, 2018 |  | September 30, 2017
Millions |  | Net realized (losses) gains |  | Net foreign exchange gains (losses) |  | Total net realized (losses) gains reflected in earnings |  | Net realized (losses) gains |  | Net foreign exchange gains (losses) |  | Total net realized gains (losses) reflected in earnings
Fixed maturity investments |  | $ | (27.6 | ) |  | $ | 18.2 |  |  | $ | (9.4 | ) |  | $ | (.4 | ) |  | $ | 2.7 |  |  | $ | 2.3 |
Short-term investments |  | (.8 | ) |  | — |  |  | (.8 | ) |  | (.1 | ) |  | — |  |  | (.1 | )
Common equity securities |  | 10.5 |  |  | — |  |  | 10.5 |  |  | 18.5 |  |  | 6.0 |  |  | 24.5 |
Other long-term investments |  | (7.0 | ) |  | (7.2 | ) |  | (14.2 | ) |  | 3.0 |  |  | (8.9 | ) |  | (5.9 | )
Net realized investment (losses) gains, pre-tax |  | (24.9 | ) |  | 11.0 |  |  | (13.9 | ) |  | 21.0 |  |  | (.2 | ) |  | 20.8 |
Income tax benefit (expense) attributable to net realized investment (losses) gains |  | 11.2 |  |  | — |  |  | 11.2 |  |  | (3.6 | ) |  | — |  |  | (3.6 | )
Net realized investment (losses) gains, after-tax |  | $ | (13.7 | ) |  | $ | 11.0 |  |  | $ | (2.7 | ) |  | $ | 17.4 |  |  | $ | (.2 | ) |  | $ | 17.2 |
Schedule of unrealized gain (loss) on investments | The following tables present net unrealized investment gains (losses) and changes in the carrying value of investments measured at fair value for the three and nine months ended September 30, 2018 and 2017:
|  | Three Months Ended |  | Three Months Ended
|  | September 30, 2018 |  | September 30, 2017
Millions |  | Net unrealized gains (losses) |  | Net foreign exchange losses |  | Total net unrealized gains (losses) reflected in earnings |  | Net unrealized gains (losses) |  | Net foreign exchange gains (losses) |  | Total net unrealized gains (losses) reflected in earnings
Fixed maturity investments |  | $ | 1.5 |  |  | $ | — |  |  | $ | 1.5 |  |  | $ | 2.0 |  |  | $ | 5.1 |  |  | $ | 7.1 |
Short-term investments |  | (.1 | ) |  | — |  |  | (.1 | ) |  | — |  |  | — |  |  | — |
Common equity securities |  | 54.9 |  |  | — |  |  | 54.9 |  |  | 26.6 |  |  | (3.1 | ) |  | 23.5 |
Other long-term investments |  | 20.1 |  |  | (.1 | ) |  | 20.0 |  |  | (2.5 | ) |  | (2.4 | ) |  | (4.9 | )
Net unrealized investment gains (losses), pre-tax |  | 76.4 |  |  | (.1 | ) |  | 76.3 |  |  | 26.1 |  |  | (.4 | ) |  | 25.7 |
Income tax expense attributable to net unrealized investment gains (losses) |  | (12.0 | ) |  | — |  |  | (12.0 | ) |  | (3.3 | ) |  | — |  |  | (3.3 | )
Net unrealized investment gains (losses), after-tax |  | $ | 64.4 |  |  | $ | (.1 | ) |  | $ | 64.3 |  |  | $ | 22.8 |  |  | $ | (.4 | ) |  | $ | 22.4 |
|  | Nine Months Ended |  | Nine Months Ended
|  | September 30, 2018 |  | September 30, 2017
Millions |  | Net unrealized (losses) gains |  | Net foreign exchange (losses) gains |  | Total net unrealized (losses) gains reflected in earnings |  | Net unrealized gains |  | Net foreign exchange gains (losses) |  | Total net unrealized gains (losses) reflected in earnings
Fixed maturity investments |  | $ | (15.7 | ) |  | $ | (14.8 | ) |  | $ | (30.5 | ) |  | $ | 19.4 |  |  | $ | 12.6 |  |  | $ | 32.0 |
Short-term investments |  | (.1 | ) |  | — |  |  | (.1 | ) |  | — |  |  | — |  |  | — |
Common equity securities |  | 43.7 |  |  | — |  |  | 43.7 |  |  | 53.5 |  |  | — |  |  | 53.5 |
Other long-term investments |  | 20.5 |  |  | 3.2 |  |  | 23.7 |  |  | 9.2 |  |  | (13.0 | ) |  | (3.8 | )
Net unrealized investment gains (losses), pre-tax |  | 48.4 |  |  | (11.6 | ) |  | 36.8 |  |  | 82.1 |  |  | (.4 | ) |  | 81.7 |
Income tax expense attributable to net unrealized investment gains (losses) |  | (17.1 | ) |  | — |  |  | (17.1 | ) |  | (5.9 | ) |  | — |  |  | (5.9 | )
Net unrealized investment gains (losses), after-tax |  | $ | 31.3 |  |  | $ | (11.6 | ) |  | $ | 19.7 |  |  | $ | 76.2 |  |  | $ | (.4 | ) |  | $ | 75.8 |
Net unrealized investment gains (losses) for Level 3 investments | The following table presents total gains (losses) included in earnings attributable to net unrealized investment gains (losses) for Level 3 investments for the three and nine months ended September 30, 2018 and 2017:
|  | Three Months Ended |  | Nine Months Ended
|  | September 30, |  | September 30,
Millions |  | 2018 |  | 2017 |  | 2018 |  | 2017
Other long-term investments |  | $ | 4.0 |  |  | $ | (.7 | ) |  | $ | 2.1 |  |  | $ | (2.2 | )
Total net unrealized investment gains (losses) , pre-tax - Level 3 investments |  | $ | 4.0 |  |  | $ | (.7 | ) |  | $ | 2.1 |  |  | $ | (2.2 | )
Investment holdings, equity securities, convertible fixed maturities and other long-term investments | The following tables present the cost or amortized cost, gross unrealized investment gains (losses), net foreign currency gains and carrying values of White Mountains’s fixed maturity investments as of September 30, 2018 and December 31, 2017.
|  | September 30, 2018
Millions |  | Cost or amortized cost |  | Gross unrealized gains |  | Gross unrealized losses |  | Net foreign currency gains |  | Carrying value
U.S. Government and agency obligations |  | $ | 127.0 |  |  | $ | — |  |  | $ | (1.6 | ) |  | $ | — |  |  | $ | 125.4 |
Debt securities issued by corporations |  | 509.4 |  |  | .2 |  |  | (9.6 | ) |  | — |  |  | 500.0 |
Mortgage and asset-backed securities |  | 132.4 |  |  | — |  |  | (3.9 | ) |  | — |  |  | 128.5 |
Municipal obligations |  | 281.1 |  |  | .4 |  |  | (3.5 | ) |  | — |  |  | 278.0 |
Total fixed maturity investments |  | $ | 1,049.9 |  |  | $ | .6 |  |  | $ | (18.6 | ) |  | $ | — |  |  | $ | 1,031.9 |
|  | December 31, 2017
Millions |  | Cost or amortized cost |  | Gross unrealized gains |  | Gross unrealized losses |  | Net foreign currency gains |  | Carrying value
U.S. Government and agency obligations |  | $ | 297.8 |  |  | $ | — |  |  | $ | (1.3 | ) |  | $ | — |  |  | $ | 296.5 |
Debt securities issued by corporations |  | 867.6 |  |  | 2.9 |  |  | (4.3 | ) |  | 14.7 |  |  | 880.9 |
Mortgage and asset-backed securities |  | 697.2 |  |  | 1.6 |  |  | (4.1 | ) |  | — |  |  | 694.7 |
Municipal obligations |  | 252.0 |  |  | 3.7 |  |  | (.8 | ) |  | — |  |  | 254.9 |
Foreign government, agency and provincial obligations |  | 2.6 |  |  | — |  |  | — |  |  | .1 |  |  | 2.7 |
Total fixed maturity investments |  | $ | 2,117.2 |  |  | $ | 8.2 |  |  | $ | (10.5 | ) |  | $ | 14.8 |  |  | $ | 2,129.7 |
The following tables present the cost or amortized cost, gross unrealized investment gains (losses), net foreign currency losses, and carrying values of White Mountains’s common equity securities and other long-term investments as of September 30, 2018 and December 31, 2017:
|  | September 30, 2018
Millions |  | Cost or amortized cost |  | Gross unrealized gains |  | Gross unrealized losses |  | Net foreign currency losses |  | Carrying value
Common equity securities |  | $ | 873.4 |  |  | $ | 171.1 |  |  | $ | (1.0 | ) |  | $ | — |  |  | $ | 1,043.5 |
Other long-term investments |  | $ | 303.8 |  |  | $ | 34.8 |  |  | $ | (47.2 | ) |  | $ | (1.7 | ) |  | $ | 289.7 |
|  | December 31, 2017
Millions |  | Cost or amortized cost |  | Gross unrealized gains |  | Gross unrealized losses |  | Net foreign currency losses |  | Carrying value
Common equity securities |  | $ | 739.7 |  |  | $ | 129.4 |  |  | $ | (3.0 | ) |  | $ | — |  |  | $ | 866.1 |
Other long-term investments |  | $ | 246.6 |  |  | $ | 6.8 |  |  | $ | (39.7 | ) |  | $ | (4.9 | ) |  | $ | 208.8 |
Other Long-Term Investments The following table presents the carrying values of White Mountains’s other long-term investments as of September 30, 2018 and December 31, 2017:
|  | Carrying Value at
Millions |  | September 30, 2018 |  | December 31, 2017
Hedge funds and private equity funds, at fair value |  | $ | 151.6 |  |  | $ | 125.3 |
Private equity securities, at fair value (1)(2) |  | 126.4 |  |  | 83.2 |
Foreign currency forward contracts |  | — |  |  | (3.7 | )
Other |  | 11.7 |  |  | 4.0 |
Total other long-term investments |  | $ | 289.7 |  |  | $ | 208.8 |
(1) See Fair Value Measurements by Level table. (2) Includes White Mountains's non-controlling interests in common equity securities, limited liability companies and private convertible preferred securities.
Other long-term investments | The following table presents investments in hedge funds and private equity funds by investment objective and sector as of September 30, 2018 and December 31, 2017:
|  | September 30, 2018 |  | December 31, 2017
Millions |  | Fair Value |  | Unfunded Commitments |  | Fair Value |  | Unfunded Commitments
Hedge funds |  |  |  |  |  |  |  |  |  |  |  |
Long/short banks and financials |  | $ | 59.6 |  |  | $ | — |  |  | $ | 54.9 |  |  | $ | — |
Total hedge funds |  | 59.6 |  |  | — |  |  | 54.9 |  |  | — |
Private equity funds |  |  |  |  |  |  |  |  |  |  |  |
Manufacturing/Industrial |  | 49.6 |  |  | 10.5 |  |  | 43.3 |  |  | 10.4 |
Aerospace/Defense/Government |  | 25.5 |  |  | 34.9 |  |  | 15.8 |  |  | 12.9 |
Direct lending |  | 10.6 |  |  | 19.9 |  |  | 7.1 |  |  | 23.1 |
Financial services |  | 6.3 |  |  | 15.7 |  |  | 4.2 |  |  | 11.7 |
Real estate |  | — |  |  | 50.0 |  |  | — |  |  | — |
Total private equity funds |  | 92.0 |  |  | 131.0 |  |  | 70.4 |  |  | 58.1 |
Total hedge funds and private equity funds included in other long-term investments |  | $ | 151.6 |  |  | $ | 131.0 |  |  | $ | 125.3 |  |  | $ | 58.1 |
Fair Value of private equity funds subject to lock-up periods | The following table presents investments in private equity funds that were subject to lock-up periods as of September 30, 2018:
Millions |  | 1 – 3 years |  | 3 – 5 years |  | 5 – 10 years |  | >10 years |  | Total
Private equity funds — expected lock-up period remaining |  | $14.2 |  | $5.0 |  | $55.9 |  | $16.9 |  | $92.0
Fair value measurements by level, investment securities | The following tables present White Mountains’s fair value measurements for investments as of September 30, 2018 and December 31, 2017 by level. The major security types were based on the legal form of the securities. White Mountains has disaggregated its fixed maturity investments based on the issuing entity type, which impacts credit quality, with debt securities issued by U.S. Government entities carrying minimal credit risk, while the credit and other risks associated with other issuers, such as corporations, foreign governments, municipalities or entities issuing mortgage and asset-backed securities vary depending on the nature of the issuing entity type. White Mountains further disaggregates debt securities issued by corporations and common equity securities by industry sector because investors often reference commonly used benchmarks and their subsectors to monitor risk and performance. Accordingly, White Mountains has further disaggregated these asset classes into subclasses based on the similar sectors and industry classifications it uses to evaluate investment risk and performance against commonly used benchmarks, such as the Bloomberg Barclays U.S. Intermediate Aggregate and S&P 500 indices.
|  | September 30, 2018
Millions |  | Fair Value |  | Level 1 |  | Level 2 |  | Level 3
Fixed maturity investments: |  |  |  |  |  |  |  |  |  |  |  |
U.S. Government and agency obligations |  | $ | 125.4 |  |  | $ | 125.4 |  |  | $ | — |  |  | $ | — |
Debt securities issued by corporations: |  |  |  |  |  |  |  |  |
Financials |  | 145.9 |  |  | — |  |  | 145.9 |  |  | — |
Consumer |  | 84.2 |  |  | — |  |  | 84.2 |  |  | — |
Technology |  | 60.4 |  |  | — |  |  | 60.4 |  |  | — |
Energy |  | 54.6 |  |  | — |  |  | 54.6 |  |  | — |
Healthcare |  | 53.9 |  |  | — |  |  | 53.9 |  |  | — |
Industrial |  | 39.5 |  |  | — |  |  | 39.5 |  |  | — |
Communications |  | 22.4 |  |  | — |  |  | 22.4 |  |  | — |
Materials |  | 22.2 |  |  | — |  |  | 22.2 |  |  | — |
Utilities |  | 16.9 |  |  | — |  |  | 16.9 |  |  | — |
Total debt securities issued by corporations |  | 500.0 |  |  | — |  |  | 500.0 |  |  | — |
Mortgage and asset-backed securities |  | 128.5 |  |  | — |  |  | 128.5 |  |  | — |
Municipal obligations |  | 278.0 |  |  | — |  |  | 278.0 |  |  | — |
Total fixed maturity investments |  | 1,031.9 |  |  | 125.4 |  |  | 906.5 |  |  | — |
Short-term investments(1) |  | 313.7 |  |  | 300.7 |  |  | 13.0 |  |  | — |
Common equity securities: |  |  |  |  |  |  |  |  |  |  |  |
Exchange traded funds (2) |  | 742.9 |  |  | 675.3 |  |  | 67.6 |  |  | — |
Technology |  | 16.8 |  |  | 16.8 |  |  | — |  |  | — |
Financials |  | 16.7 |  |  | 16.7 |  |  | — |  |  | — |
Healthcare |  | 16.4 |  |  | 16.4 |  |  | — |  |  | — |
Industrial |  | 15.6 |  |  | 15.6 |  |  | — |  |  | — |
Communications |  | 14.8 |  |  | 14.8 |  |  | — |  |  | — |
Consumer |  | 9.8 |  |  | 9.8 |  |  | — |  |  | — |
Energy |  | 6.6 |  |  | 6.6 |  |  | — |  |  | — |
Other (3) |  | 203.9 |  |  | — |  |  | 203.9 |  |  | — |
Total common equity securities |  | 1,043.5 |  |  | 772.0 |  |  | 271.5 |  |  | — |
Other long-term investments (4) |  | 138.1 |  |  | — |  |  | — |  |  | 138.1 |
Total investments |  | $ | 2,527.2 |  |  | $ | 1,198.1 |  |  | $ | 1,191.0 |  |  | $ | 138.1 |
(1) Short-term investments are measured at amortized cost, which approximates fair value. (2) ETFs traded on foreign exchanges are priced using the fund's published NAV to account for the difference in market close times and are therefore designated a level 2 measurement. (3) Consists of two investments in unit trusts that primarily invest in international equities. (4) Excludes carrying value of $151.6 associated with hedge funds and private equity funds for which fair value is measured at NAV using the practical expedient.
|  | December 31, 2017
Millions |  | Fair Value |  | Level 1 |  | Level 2 |  | Level 3
Fixed maturity investments: |  |  |  |  |  |  |  |  |  |  |  |
U.S. Government and agency obligations |  | $ | 296.5 |  |  | $ | 296.5 |  |  | $ | — |  |  | $ | — |
Debt securities issued by corporations: |  |  |  |  |  |  |  |  |  |  |  |
Consumer |  | 185.1 |  |  | — |  |  | 185.1 |  |  | — |
Communications |  | 127.8 |  |  | — |  |  | 127.8 |  |  | — |
Financials |  | 114.8 |  |  | — |  |  | 114.8 |  |  | — |
Utilities |  | 108.9 |  |  | — |  |  | 108.9 |  |  | — |
Materials |  | 95.5 |  |  | — |  |  | 95.5 |  |  | — |
Healthcare |  | 94.3 |  |  | — |  |  | 94.3 |  |  | — |
Technology |  | 80.5 |  |  | — |  |  | 80.5 |  |  | — |
Energy |  | 48.1 |  |  | — |  |  | 48.1 |  |  | — |
Industrial |  | 25.9 |  |  | — |  |  | 25.9 |  |  | — |
Total debt securities issued by corporations |  | 880.9 |  |  | — |  |  | 880.9 |  |  | — |
Mortgage and asset-backed securities |  | 694.7 |  |  | — |  |  | 694.7 |  |  | — |
Municipal obligations |  | 254.9 |  |  | — |  |  | 254.9 |  |  | — |
Foreign government, agency and provincial obligations |  | 2.7 |  |  | — |  |  | 2.7 |  |  | — |
Total fixed maturity investments |  | 2,129.7 |  |  | 296.5 |  |  | 1,833.2 |  |  | — |
Short-term investments (1) |  | 176.1 |  |  | 151.0 |  |  | 25.1 |  |  | — |
Common equity securities: |  |  |  |  |  |  |  |  |  |  |  |
Exchange traded funds (2) |  | 569.7 |  |  | 508.1 |  |  | 61.6 |  |  | — |
Healthcare |  | 17.1 |  |  | 17.1 |  |  | — |  |  | — |
Financials |  | 16.3 |  |  | 16.3 |  |  | — |  |  | — |
Technology |  | 15.1 |  |  | 15.1 |  |  | — |  |  | — |
Industrial |  | 11.9 |  |  | 11.9 |  |  | — |  |  | — |
Communications |  | 10.9 |  |  | 10.9 |  |  | — |  |  | — |
Consumer |  | 10.7 |  |  | 10.7 |  |  | — |  |  | — |
Energy |  | 3.8 |  |  | 3.8 |  |  | — |  |  | — |
Other (3) |  | 210.6 |  |  | — |  |  | 210.6 |  |  | — |
Total common equity securities |  | 866.1 |  |  | 593.9 |  |  | 272.2 |  |  | — |
Other long-term investments (4) |  | 87.2 |  |  | — |  |  | — |  |  | 87.2 |
Total investments |  | $ | 3,259.1 |  |  | $ | 1,041.4 |  |  | $ | 2,130.5 |  |  | $ | 87.2 |
(1) Short-term investments are measured at amortized cost, which approximates fair value. (2) ETFs traded on foreign exchanges are priced using the fund’s published NAV to account for the difference in market close times and are therefore designated a level 2 measurement. (3) Consists of two investments in unit trusts that primarily invests in international equities. (4) Excludes carrying value of $(3.7) related to foreign currency forward contracts and $125.3 associated with hedge funds and private equity funds for which fair value is measured at NAV using the practical expedient.
Debt securities issued by corporations, credit ratings | The following table presents the ratings of debt securities issued by corporations held in White Mountains’s investment portfolio as of September 30, 2018 and December 31, 2017:
|  | Fair Value at
Millions |  | September 30, 2018 |  | December 31, 2017
AAA |  | $ | 8.1 |  |  | $ | 1.6 |
AA |  | 83.6 |  |  | 42.6 |
A |  | 273.3 |  |  | 192.5 |
BBB |  | 135.0 |  |  | 465.2 |
BB |  | — |  |  | 161.7 |
B |  | — |  |  | 17.3 |
Debt securities issued by corporations (1) |  | $ | 500.0 |  |  | $ | 880.9 |
(1) Credit ratings are assigned based on the following hierarchy: (1) Standard & Poor’s Financial Services LLC (“S&P”) and (2) Moody's Investor Service, Inc. (“Moody’s”).
Mortgage-backed, asset-backed securities | The following table presents the fair value of White Mountains’s mortgage and asset-backed securities as of September 30, 2018 and December 31, 2017:
|  | September 30, 2018 |  | December 31, 2017
Millions |  | Fair Value |  | Level 2 |  | Level 3 |  | Fair Value |  | Level 2 |  | Level 3
Mortgage-backed securities: |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Agency: |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
GNMA |  | $ | 24.5 |  |  | $ | 24.5 |  |  | $ | — |  |  | $ | 46.3 |  |  | $ | 46.3 |  |  | $ | — |
FNMA |  | 53.6 |  |  | 53.6 |  |  | — |  |  | 84.5 |  |  | 84.5 |  |  | — |
FHLMC |  | 39.0 |  |  | 39.0 |  |  | — |  |  | 62.0 |  |  | 62.0 |  |  | — |
Total agency (1) |  | 117.1 |  |  | 117.1 |  |  | — |  |  | 192.8 |  |  | 192.8 |  |  | — |
Non-agency: |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Commercial |  | — |  |  | — |  |  | — |  |  | 70.5 |  |  | 70.5 |  |  | — |
Total non-agency |  | — |  |  | — |  |  | — |  |  | 70.5 |  |  | 70.5 |  |  | — |
Total mortgage-backed securities |  | 117.1 |  |  | 117.1 |  |  | — |  |  | 263.3 |  |  | 263.3 |  |  | — |
Other asset-backed securities: |  |  |  |  |  |  |  |  |  |  |  |  |  |
Credit card receivables |  | 8.9 |  |  | 8.9 |  |  | — |  |  | 206.0 |  |  | 206.0 |  |  | — |
Vehicle receivables |  | 2.5 |  |  | 2.5 |  |  | — |  |  | 142.4 |  |  | 142.4 |  |  | — |
Other |  | — |  |  | — |  |  | — |  |  | 83.0 |  |  | 83.0 |  |  | — |
Total other asset-backed securities |  | 11.4 |  |  | 11.4 |  |  | — |  |  | 431.4 |  |  | 431.4 |  |  | — |
Total mortgage and asset-backed securities |  | $ | 128.5 |  |  | $ | 128.5 |  |  | $ | — |  |  | $ | 694.7 |  |  | $ | 694.7 |  |  | $ | — |
(1) Represents publicly traded mortgage-backed securities which carry the full faith and credit guaranty of the U.S. Government (i.e., GNMA) or are guaranteed by a government sponsored entity (i.e., FNMA, FHLMC).
Non-agency commercial mortgage securities, type of interest rate and tranche levels |
Rollforward of fair value investments by level | The following tables present the changes in White Mountains’s fair value measurements by level for the nine months ended September 30, 2018 and 2017:
|  |  | Level 3 Investments |
Millions | Level 1 investments | Level 2 investments | Fixed maturity investments | Other long-term investments | Hedge Funds and Private Equity Funds measured at NAV(3) |  | Total |
Balance at December 31, 2017 | $ | 890.4 |  | $ | 2,105.4 |  | $ | — |  | $ | 87.2 |  | $ | 125.3 |  |  | $ | 3,208.3 |  | (1)(2)
Net realized and unrealized gains (losses) | 51.9 |  | (33.6 | ) | — |  | (4.2 | ) | 17.2 |  |  | 31.3 |  | (4)
Amortization/Accretion | .1 |  | (2.3 | ) | — |  | — |  | — |  |  | (2.2 | ) |
Purchases | 412.6 |  | 673.5 |  | — |  | 55.1 |  | 10.7 |  |  | 1,151.9 |  |
Sales | (457.6 | ) | (1,565.0 | ) | — |  | — |  | (1.6 | ) |  | (2,024.2 | ) |
Transfers in | — |  | — |  | — |  | — |  | — |  |  | — |  |
Transfers out | — |  | — |  | — |  | — |  | — |  |  | — |  |
Balance at September 30, 2018 | $ | 897.4 |  | $ | 1,178.0 |  | $ | — |  | $ | 138.1 |  | $ | 151.6 |  |  | $ | 2,365.1 |  | (2)
(1) Excludes carrying value of $(3.7) as of December 31, 2017 associated with foreign currency forward contracts. (2) Excludes carrying value of $176.1 and $313.7 at December 31, 2017 and September 30, 2018 classified as short-term investments. (3) Investments for which fair value is measured at NAV using the practical expedient are no longer classified within the fair value hierarchy. See Note 1 — “Basis of Presentation and Significant Accounting Policies”. (4) Excludes realized and unrealized losses associated with foreign currency forward contracts, foreign currency on cash and open trades and short-term investments of $3.5, $4.2 and $0.7 for the nine months ended September 30, 2018.
|  |  | Level 3 Investments |  |  |
Millions | Level 1 investments | Level 2 investments | Fixed maturity investments | Other long-term investments | Hedge Funds and Private Equity Funds measured at NAV(3) | Total |
Balance at December 31, 2016 | $ | 279.5 |  | $ | 2,093.8 |  | $ | — |  | $ | 91.4 |  | $ | 82.6 |  | $ | 2,547.3 |  | (1)(2)(4)
Net realized and unrealized gains (losses) | 52.4 |  | 59.8 |  | — |  | (2.2 | ) | 15.6 |  | 125.6 |  | (5)
Amortization/Accretion | — |  | (6.6 | ) | — |  | — |  | — |  | (6.6 | ) |
Purchases | 940.7 |  | 1,038.5 |  | 31.2 |  | 2.9 |  | 64.9 |  | 2,078.2 |  |
Sales | (539.0 | ) | (1,668.2 | ) | (12.5 | ) | (2.0 | ) | (8.2 | ) | (2,229.9 | ) |
Deconsolidation of SSIE | — |  | (5.2 | ) | — |  | — |  | — |  | (5.2 | ) |
Transfers in | — |  | 13.1 |  | — |  | — |  | — |  | 13.1 |  |
Transfers out | — |  | — |  | (13.1 | ) | — |  | — |  | (13.1 | ) |
Balance at September 30, 2017 | $ | 733.6 |  | $ | 1,525.2 |  | $ | 5.6 |  | $ | 90.1 |  | $ | 154.9 |  | $ | 2,509.4 |  | (1)(2)
(1) Excludes carrying value of $175.0 and $786.5 at December 31, 2016 and September 30, 2017 classified as short-term investments, of which $0.1 is classified as held for sale at December 31, 2016. (2) Excludes carrying value of $(1.2) and $(15.4) as of December 31, 2016 and September 30, 2017 associated with foreign currency forward contracts. (3) Investments for which fair value is measured at NAV using the practical expedient are no longer classified within the fair value hierarchy. See Note 1 — “Basis of Presentation and Significant Accounting Policies”. (4) Includes carrying value of $6.6 of fixed maturity investments at December 31, 2016 that is classified as assets held for sale related to SSIE. (5) Excludes realized and unrealized losses associated with foreign currency forward contracts of $23.1 for the nine months ended September 30, 2017.
Schedule of significant unobservable inputs used in estimating the fair value of investment securities | The following tables present significant unobservable inputs used in estimating the fair value of other long-term investments, other than hedge funds and private equity funds, classified within Level 3 as of September 30, 2018 and December 31, 2017. The fair value of investments in hedge funds and private equity funds are generally estimated using the NAV of the funds.
$ in millions, except share price |  | September 30, 2018
Description |  | Valuation Technique(s) |  | Fair Value (1) |  | Unobservable Input
Private equity security |  | Share price of most recent transaction |  | $28.3 |  | Share price | - | $56.60
Private equity security |  | Discounted cash flow |  | $21.0 |  | Discount rate | - | 25.0%
Private equity security |  | Discounted cash flow |  | $22.1 |  | Discount rate | - | 35.0%
Private convertible preferred security |  | Discounted cash flow |  | $14.5 |  | Discount rate | - | 30.0%
Private equity security |  | Recent transaction |  | $15.8 |  | Share price | - | €338.85
Private preferred security |  | Multiple of EBITDA |  | $3.5 |  | EBITDA multiple | - | 6.00
Private debt instrument |  | Discounted cash flow |  | $10.5 |  | Discount rate | - | 9.62%
(1) Includes the net unrealized investment gains (losses) associated with foreign currency; foreign currency effects based on observable inputs.
$ in millions, except share price |  | December 31, 2017
Description |  | Valuation Technique(s) |  | Fair Value (1) |  | Unobservable Input
Private equity security |  | Discounted cash flow |  | $21.0 |  | Discount rate | - | 25.0%
Private equity security |  | Discounted cash flow |  | $22.1 |  | Discount rate | - | 35.0%
Private convertible preferred security |  | Discounted cash flow |  | $14.5 |  | Discount rate | - | 30.0%
Private equity security |  | Discounted cash flow/ Option pricing method |  | $11.3 |  | Discount rate | - | 21.0%
|  |  |  |  |  | Time until expiration | - | 4 years
|  |  |  | Volatility/Standard deviation | - | 50.0%
|  |  |  | Risk free rate | - | 1.77%
Private preferred security |  | Multiple of EBITDA |  | $0.6 |  | EBITDA multiple | - | 6.00
Private equity security |  | Share price of most recent transaction |  | $3.6 |  | Share price | - | $2.52
(1) Includes the net unrealized investment gains (losses) associated with foreign currency; foreign currency effects based on observable inputs.

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